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Tactics in a board game usually refer to short-term optimizations to get a better local position in the game. Strategy refers to your long-term plans, for combining the results of many shorter term interactions into a winning game.

Some games have only tactical considerations, or an emphasis on them, while some games are more amenable to long-range planning.

In the game of Go, for instance, you may study tactical issues such as life and death (whether you can save or kill a particular enclosed group) and tesuji (clever tactics for killing and splitting your opponents stones, or saving or connecting your own), while also important are strategic issue like positional judgement (figuring out in the middle game who is ahead, and where they are ahead), direction of play, and balancing between territory and influence. Effective strategic play must of course be built on solid tactical play, but it can determine who winds up having the advantage in most tactical battles, and who winds up with the most territory even if they lose small battles here and there.

The concept can apply to other games as well. Tactics will usually influence how you play best for one or a few turns in a row, while strategy guides what you are doing for the whole game; how you will win. Strategy is about what you are trying to do, and tactics how you are trying to do it.

In Settlers of Catan, some strategic options may be going for roads and settlements, to try and get the longest road and a lot of settlements (with just enough cities to allow you to build more), or your strategy may be going with cities and development cards, with just enough settlements to allow you to build the cities you need; or you might have a ports based strategy, in which you try and obtain favorable ports and can thus buy any resources you need. The tactics used to support these strategies may be somewhat different, but they will involve tricks for getting the best trade, blocking your opponent quickly so you can get to the space you need, proper placement of the robber to slow down someone else competing with you.

Strategy is the long term plan. It is how you intend to play your game, such as "the money route", "the resource route", or "the balanced route". It is your plan, its your high level approach to achieving your goal, i.e. winning the game!

Tactics are the finer detail. Your tactics are HOW you are going to achieve your strategy. If you are going "the money route", in turn X, what actions are you going to take to maximise the amount of money you get.

"Strategy without tactics is the
slowest route to victory. Tactics
without strategy is the noise before
defeat." - Sun Tzu

In general, tactics focus on short-term, local results. The strategy should instead focus on your global, long-term objectives. This is why some tactically brilliant decisions (say, an effective surprise attack) can be, in the end, strategically detrimental.

Bear in mind that in wargames, tactics and strategy have exactly the same meaning as they do in the military. In fact, when it comes to tactics, questions you often need to ask in a game are "how does this game implement concentration of force" or "where is a good spot in game terms to keep a reserve" - which can all be strongly affected by things like ZOC rules, and the ability of the enemy to concentrate firepower on stacked units.

Strategic considerations may be out of scope of the game, but when you're playing something like World in Flames then, you need to build plans and flex them on the fly.

Strategy is a plan. Tactics are the details used to implement that plan.

In Puerto Rico, you may have a building strategy, this might lead you to use tactics in the beginning like getting quarries, and buying buildings that will help you make money. A shipping strategy may have you use the tactic of pulling corn when settler comes up.